Radial basis function based finite element method

Formulation and applications

authored by: Dung Nguyen KIEN, Xiaoying ZHUANG
Abstract: In the study, a method is proposed and developed for solid analysis that is a hybrid of the radial basis function and the finite element method (RBF-FEM). Based on the finite nodes, the method employs the radial basis functions to produce the shape functions with simplicity, especially when increasing the element node number. The formulation and applications of the method in the analysis of solids are examined. Several numerical examples are carried out to analyze the convergence, accuracy, and computational time cost. Its comeouts are then compared with that by the finite element method. The study also shows the factors that affect the accuracy of the method, such as the radial basis function types, radial basis function shape parameter, node number, and node position in an element. It is shown that the method quickly produces better results with large-node-number elements (seven and eight nodes) in comparison to the conventional numerical method. Discussion on the method and the extensibility of the approach are addressed in the conclusion.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 152
Pages: 455-472
No. of pages: 18
ISSN: 0955-7997
Publication date: 07.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, General Engineering, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2023.04.014 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{913e09798e244617be3a88af4ab1ddda,
title = "Radial basis function based finite element method: Formulation and applications",
abstract = "In the study, a method is proposed and developed for solid analysis that is a hybrid of the radial basis function and the finite element method (RBF-FEM). Based on the finite nodes, the method employs the radial basis functions to produce the shape functions with simplicity, especially when increasing the element node number. The formulation and applications of the method in the analysis of solids are examined. Several numerical examples are carried out to analyze the convergence, accuracy, and computational time cost. Its comeouts are then compared with that by the finite element method. The study also shows the factors that affect the accuracy of the method, such as the radial basis function types, radial basis function shape parameter, node number, and node position in an element. It is shown that the method quickly produces better results with large-node-number elements (seven and eight nodes) in comparison to the conventional numerical method. Discussion on the method and the extensibility of the approach are addressed in the conclusion.",
keywords = "Finite element method, Numerical method, Radial basis function, Solid mechanics",
author = "KIEN, {Dung Nguyen} and Xiaoying ZHUANG",
year = "2023",
month = jul,
doi = "10.1016/j.enganabound.2023.04.014",
language = "English",
volume = "152",
pages = "455--472",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}

Back